Number Theory seminar
Tuesday, January 16, 16:00 - 17:00
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Venue: Room 105
Host: Ravi Raghunathan
Speaker: Surya Ramana
Affiliation: Harish-Chandra Research Institute
Title: An Improved Bound for the Additive Energy of Large Sets of Prime Numbers
Abstract: When A and B are subsets the integers, the additive energy of A and B is the quantity E(A,B) defined by E(A,B) = | { (x_1,x_2,y_1, y_2) \in A\times A \times B \times B\, | x_1 +y_1 = x_2 +y_2 } | Additive energy is a basic notion in additive number theory and additive combinatorics. Given $\alpha$ in $(0,1)$ and $\lambda >0$ and a large enough integer $N$, we obtain an essentially optimal upper bound for the additive energy $E(A,B)$ of any subsets $A$ and $B$ of the prime numbers in the intervals $[1, N]$ and $[1, \lambda N]$ respectively, when $A$ satisfies $|A| \geq \alpha N$. This is based on work with K. Mallesham and Gyan Prakash.